Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+6y &= 4 \\ 3x+3y &= 2\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -3x+2$ Divide both sides by $3$ to isolate $y$ $y = {-x + \dfrac{2}{3}}$ Substitute this expression for $y$ in the first equation. $2x+6({-x + \dfrac{2}{3}}) = 4$ $2x - 6x + 4 = 4$ Simplify by combining terms, then solve for $x$ $-4x + 4 = 4$ $-4x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $2( 0)+6y = 4$ $6y = 4$ $6y = 4$ $y = \dfrac{2}{3}$ The solution is $\enspace x = 0, \enspace y = \dfrac{2}{3}$.